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I have seen several responses to this article;  none seemed to give
a clear answer to simple problem.
In article <3794@oberon.USC.EDU> mathur@pollux.usc.edu (Samir Kumar Mathur) writes:
)Here is a thought experiment which seems to violate Uncertainity Principle (UP)
)that came up at a casual discussion with a friend.
)
)Scenario : 
)	There are two particles A and B and I am trying to measure their
)	momentum and positions accurately.
)
)Experiment :
)	(1) At time t:
)		(a) I measure the momentums p(A,t) & p(B,t) and hence
)			p(A&B,t) = p(A,t) + p(B,t) as accurately as I wish.
Possible
)
)	(2) At time t+dt:
)		(a) I measure the momentum of A, p(A,t+dt) as accurately
)			as I wish.
Possible
)		(b) I measure the position of B, q(B,t+dt) as accurately
)			as I wish.
Possible.  However, when dealing with possible violations of the 
uncertainty principle, it is best to use the technique Bohr used 
in his debates with Einstein:  be as concrete as possible.  Do not 
just say "measure the position";  say how one is doing it.  In this
case, say that the measurement is made visually, by shining a light
on it.  (Which can be done as accurately as one wishes.)
)		(c) I calculate p(B,t+dt) = p(A&B,t) - p(A,t+dt) 
)			{conservation of momentum} as accurately as I wish.
Oh.  At this point, realize that "shining a light on it" is not
the phrase a physicist would use.  A physicist would say "scattering
light off it".  This practically shouts out what is going on in this
problem.  What does "scattering light off it" mean?  It means that 
one is shining a light on the, and seeing which photon bounce off
particle B. Bounce off?  What does this do to the momentum of particle 
B?  It changes it by an unknown amount;  the uncertainty of your 
knowledge of the momentum of particle B will be greater than or equal 
to h divided by the uncertainty with which you know its position.  At 
this point, one can dispense with the concrete example, and realize
that this will be the case no matter what method was used to measure
the position of particle B;  any method would have change the particle's
momentum.  One does know what the momentum of particle B was before you 
measured its position, p(B), but this information is of no use in predicting
the particle's motion after the position measurement.

  This is not one of the possible explanations that you gave --  one can
measure momentum and not disturb the momentum -- it is measuring position 
that disturbs the momentum.  Conservation of momentum is not a problem 
because the system is not just particle A and particle B -- there is, in 
addition, whatever measures the position of particle B.

I hope that this answer is reasonably clear;  please let me know if it
was not.
-- 
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Courtenay Footman		ARPA:	cpf@lnssun9.tn.cornell.edu
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